Abstract
We consider the calculation of electromagnetic fields generated by an electron bunch passing through a vacuum chamber structure that, in general, consists of an entry pipe, followed by some kind of transition or cavity, and ending in an exit pipe. We limit our study to structures having rectangular cross-section, where the height can vary as function of longitudinal coordinate but the width and side walls remain fixed. For such structures, we derive a Fourier representation of the wake potentials through one-dimensional functions. A new numerical approach for calculating the wakes in such structures is proposed and implemented in the computer code ECHO(2D). The computation resource requirements for this approach are moderate and comparable to those for finding the wakes in 2D rotationally symmetric structures. Numerical examples obtained with the new numerical code are presented.
Highlights
The interaction of charged particle beams and the vacuum chamber environment can be quantified using the concept of impedance or wakefield [1]
Many three-dimensional vacuum chamber components used in particle accelerators can be well-approximated with structures of rectangular cross section whose height can vary as function of longitudinal coordinate but whose width and side walls remain fixed
In this paper we presented a new method for solving electromagnetic problems and calculating wakefields excited by a relativistic bunch in a structure that is characterized by a rectangular cross-section whose height can vary as function of longitudinal coordinate but whose width and side walls remain fixed
Summary
SLAC National Accelerator Laboratory, Stanford University, Stanford, California 94309, USA (Received 31 July 2015; published 19 October 2015). We limit our study to structures having rectangular cross section, where the height can vary as function of longitudinal coordinate but the width and side walls remain fixed. For such structures, we derive a Fourier representation of the wake potentials through one-dimensional functions. A new numerical approach for calculating the wakes in such structures is proposed and implemented in the computer code ECHO(2D). The computation resource requirements for this approach are moderate and comparable to those for finding the wakes in 2D rotationally symmetric structures. Numerical examples obtained with the new numerical code are presented
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